Finite-time Consensus Control For Second-order Multi-agent Systems

The coordination control of multi-agent systems(MAS)has received much attentions in the past decades.Its wide applications can be found in diverse areas,including formation control of multi-robots,flocking,swarming,and attitude alignment.The consensus problem is the typical issue of MAS,which aims at designing a consensus protocol such that a team of agents can achieve an agreement.In the consensus control of MAS,the convergence rate is an important indicator for the dynamic behaviors of agents.The finite-time control offers higher accuracy and faster response.The best way to deal with the finite-time problem is sliding mode control,this paper investigates the finite-time consensus problem based on the sliding mode control and the details are as follows:Firstly,the finite-time consensus problem for second-order MAS with known and unknown velocities.A finite-time protocol with relative position measurements and velocity measurements is proposed for MAS.Based on the super twisting sliding mode algorithm,a finite-time observer is proposed to estimate the velocity measurements.On the basis of Lyapunov stability theorem and homogeneous theory,it is proved that the consensus can be achieved in finite time.Secondly,this paper investigates the finite-time consensus problem for second-order MAS with unknown velocities and disturbances.By introducing the second-order sliding mode observer,two novel distributed finite-time protocols with only relative position measurements are proposed.When the boundaries of disturbances are unknown,a new observer is proposed by using the adaptive super twisting sliding mode,what's more,a finite-time controller is studied based on the super twisting sliding mode and integral sliding mode.It is proved that the consensus can be achieved in finite time with the help of Lyapunov stability theorem and homogeneous theory.Finally,the simulation examples are provided to show the effectiveness of the theoretical results.